I87 is an excellent highway and has been voted the National "most scenic" highway several times. The grades aren't real steep - more like a series of long rolling hills - and you should have no difficulties.
Lake George is a destination spot and has several campgrounds that cater to families. Busy in the summer months. Tell us more about what you are looking for in a campround. Amenities, in-town location, privacy, big rig sites, wifi, satelite access, etc.???
Perhaps the nicest of the bunch is the Lake George RV Park on Rt 149, 1 mile off I87 at exit 20. Not to be confused with the Lake George Escape Campground or the Lake George Campground, all different places with nearly identical names!. The Lake George RV Park is pricey (I think around $55 in the peak summer months) but has the best and most elegant facilities in the area. See http://www.lakegeorgervpark.com/
There is a NY State Park on the lake a short way north of Lake George. Very busy in the summer and sometimes noisy, but the rates are the lowest aroud.
If you want rural privacy in a quiet campground, try Daggett Lake Campsites outside of Warrensburg. It's on a private lake and is very strictly run to maintain its natural environment and assure peace and quiet. The owners also operate a water skiing service on their private lake. See http://www.daggettlake.com/